A multivariate probit latent variable model for analyzing dichotomous responses

We propose a multivariate probit model that is defined by a confirmatory factor analysis model with covariates for analyzing dichotomous data in medical research. Our proposal is a generalization of several useful multivariate probit models, and provides a flexible framework for practical applications. We implement a Monte Carlo EM algorithm for maximum likelihood estimation of the model, and develop a path sampling procedure to compute the observed-data log-likelihood for evaluating the Bayesian Information Criterion for model comparison. Our methodology is illustrated by analyzing two data sets in medical research.